Amid injuries to Lucas Biglia, Stefan Radu, Bastos, goalkeeper Federico Marchetti and Dusan Basta, Lazio coach Simeone Inzaghi had to tinker for the trip north to Udinese' Dacia stadium.
But with Immobile spearheading the visitors' attack and flanked by Keita and Felipe Anderson, Udinese had their work cut out.
In the end, Giuseppe Iachini's hosts had so little to offer fans started leaving a half-full stadium with 15 minutes remaining.
Immobile headed Lazio into a 28th minute lead and, after Keita burst through to beat Orestis Karnezis minutes after the restart, the Italy international completed his brace with relative ease on the hour.
Lazio's fourth win in seven games moves them up to provisional third place at two points behind leaders Juventus.
Juventus are away to Empoli on Sunday when the champions, aiming for a record sixth consecutive league title this season, will be hoping to maintain their one-point lead on Napoli, who face Atalanta in Bergamo.
Lazio started brightly but it took until 25 minutes for them to fully settle into their stride.
Keita's daisy-cutter was deflected inches past the far post for a corner and from Anderson's delivery Sergej Milinkovic-Savic headed the ball back towards the near post where Immobile beat Karnezis with a superb bullet header.
A Rodrigo De Paul drive for the hosts flashed just wide of Thomas Strakosha's post and then Emmanuel Badu's shot was charged down.
But Lazio took a firm grip of the match only minutes into the second half.
Senad Lulic was first unlucky not to get more on the ball only 40 seconds after the restart when his toe-poke went straight to Karnezis.
Eight minutes later, a delightful ball by Anderson caught the Udinese defence out and sent Keita through to beat Karnezis with a low drive at his far post.
Immobile saw a drive from 25 yards deflected out for a corner, but minutes later he completed his brace after a superb move involving Marco Parolo and Lulic.
Earlier Saturday, a pair of second-half goals from Riccardo Meggiorini and Roberto Inglese got high-flying Chievo back to winning ways with a 2-0 defeat of struggling new boys Pescara.
Despite an impressive 10 points from their opening six games, the Flying Donkeys travelled to the Stadio Adriatico looking to make amends for last week's 2-0 defeat at Napoli.
It took until the 76th minute for the visitors to make their mark, but Meggiorini's opener signalled the end of the hosts' challenge after he was left free to latch on to Valter Birsa's smart chip to run down and beat Albano Bizzarri.
Pescara's backline was rumbled again barely 10 minutes later when Lucas Castro, from the right flank, found Inglese in space and completely unmarked to toe-poke the ball past the onrushing Bizzarri.
Chievo's fourth win in seven games left Rolando Maran's men in provisional fourth ahead of the remaining fixtures.